Middle Mantle Seismic Structure of the African Superplume

Transcription

1 Pure Appl. Geophys. Ó 2012 Springer Basel AG DOI /s y Pure and Applied Geophysics Middle Mantle Seismic Structure of the African Superplume MARTIN B. C. BRANDT 1,2 Abstract I present the results of statistical hypothesis testing of GRAND s (2002) global tomography model of three-dimensional shear velocity variations for the middle mantle underneath eastern and southern Africa. I apply an F test to evaluate the validity of a model where a tilted, slow-velocity anomaly in the deepest mantle under southern Africa, known as the African superplume, is continuous with a slow-velocity anomaly in the upper mantle under eastern Africa. This null hypothesis is tested against alternative hypotheses, in which various obstruction volumes in the middle mantle are constrained to zero perturbation from the one-dimensional reference velocity during the tomographic inversion. I find that there is an equal probability of accepting an alternative hypothesis with a thin obstruction volume at 850 1,000 km depth, whereas volumes at other depths are rejected. But the alternative hypothesis, where a connection is forced at 850 1,000 km depth, is rejected. I conclude that the African superplume rises to at least 1,150 km depth, and that the upper mantle slow-velocity anomaly continues from the surface to below the mantle transition zone. I interpret the obstruction volume as a weakening of the superplume in the middle mantle. Key words: Global tomography, African superplume, shear wave, hypothesis testing. 1. Introduction The African superplume is a strong shear velocity reduction in the lower mantle beneath southern and eastern Africa (e.g. SIMMONS et al., 2007) which consistently shows up in the three-dimensional mantle S-velocity distribution on a global scale (RITSEMA et al., 1999; MASTERS et al., 2000; MEGNIN and ROMANOWICZ, 2000; GU et al., 2001; GRAND, 2002). The superplume consists of a ridge-like structure with ultra-low velocity at its base at the 1 Seismology Unit, Council for Geoscience, Pretoria, South Africa. martinb@geoscience.org.za 2 School of Geosciences, University of the Witwatersrand, Johannesburg, South Africa. core mantle boundary, a relatively uniform 3 % reduction in shear velocity above D 00 (HELMBERGER et al., 2000), and is orientated roughly NW SE and tilts towards the east at latitudes from 15 to 30 N. There are strong velocity contrasts at the margins of 2 % over *300 km distance, which suggest a significant compositional change between the superplume and the surrounding mantle (RITSEMA et al., 1998a). By forward modelling S, ScS and SKS phases, NI and HELMBERGER (2003) estimated that the slow-velocity anomaly extends at least to 1,200 km above D 00.RITSEMA et al., (1998a) model its top at about 1,400 km depth (i.e. about 1,400 km above D 00 ). A study into the Earth s orientation relative to its spin axis determined from the nonhydrostatic inertia tensor (caused by large slow shear velocity anomalies in the mantle) has led STEINBERGER and TORSVIK (2010) to suggest a longevity for the superplume of more than *50 Ma. In the upper mantle, a km wide zone of slow velocities is seen beneath the eastern branch of the East African Rift extending into, but not necessarily through, the mantle transition zone. Shear velocity reductions greater than 3 % extend to between 100 and 150 km depth, and velocities *2.5 % slow persist to at least 400 km depth (RITSEMA et al., 1998b; NYBLADE et al., 2000). The temperature beneath the rifted lithosphere from 100 to 400 km depth is K higher than ambient mantle temperatures, consistent with the observation that the 410 km discontinuity in the region is depressed by km (VENKATARAMAN et al., 2004). To explain East African Cenozoic tectonism, one or more upper mantle plume heads have been invoked under the eastern margin of the Tanzania craton (NYBLADE et al., 2000) or the Afar region (RITSEMA and VAN HEIJST, 2000). Alternatively, passive stretching of the lithosphere may cause small-scale

2 M. B. C. Brandt Pure Appl. Geophys. convection beneath the transition from thick cratonic lithosphere to thin oceanic lithosphere or thinned continental lithosphere (KING and RITSEMA, 2000). Both of these hypotheses can explain the volcanism and gravity field of East Africa, but fail to account for the excess elevation of eastern and southern Africa known as the African superswell (LITHGOW-BERTELLONI and SILVER, 1998; FORTE et al., 2010). To explain the excess elevation of the superswell, a hypothesis has been proposed whereby the African superplume extends from the core mantle boundary under southern Africa into the slow-velocity anomaly in the upper mantle under eastern Africa (RITSEMA et al., 1999; ROMANOWICZ and GUNG, 2002). This implies that the African superplume plays a major role in supplying heat and causing mantle flow in the asthenosphere resulting in hotspot volcanism, and also that deep mantle convection supports the dynamic topography of the African Superswell (LITHGOW-BERTELLONI and SILVER, 1998; FORTE et al., 2010). However, RITSEMA et al., (1999) qualify their result: they found a weakening of the slow-velocity anomaly between 670 and 1,000 km depth, which they interpret as meaning that the upwelling is obstructed (Fig. 1). Backus Gilbert resolution kernels led them to conclude that the continuity of the slow-velocity anomaly at 2,500, 1,500 and 700 km depths is not caused by preferential SW to NE bodywave sampling. Other tomography models (e.g., GRAND, 2002; SIMMONS et al., 2007) also show a tenuous connection between the deep mantle slow velocities and the upper mantle slow anomalies seen beneath eastern Africa. The slow velocities underlying the East African Rift could be either unconnected or linked in a complex way to the deeper superplume. To put this into context: global tomographic images have revealed a variety of mantle plumes (RITSEMA and ALLEN, 2003; MONTELLI et al., 2004, 2006). At least nine hotspots, e.g., Ascension, Azores, Canary, Easter, Samoa and Tahiti, are associated with cap plumes originating near the core mantle boundary. But at least another eight, e.g., Bowie, eastern Australia, Eifel, Etna, Iceland, Cocos-Keeling, Galapagos and Juan de Fuca/Cobb, are associated with plumes whose imaged base is near the 670 km discontinuity. In addition, some plumes exist without associated hotspots, whereas the Reunion and Yellowstone hotspots have no substantial plume underneath. This has led MONTELLI et al. (2004) to suggest two convecting regions in the mantle that are separated by a thermal boundary layer and which are linked in a more complex way than either whole or layered convection models. Global tomography models still lack detailed resolution. This is apparent in the differences that still exist among models when one compares them in detail (e.g. GURNIS et al., 2000; RITSEMA et al., 1999) (Fig. 1). It is true that mantle tomography has improved significantly during the 21st century (e.g. NOLET et al., 2007). The African and Pacific superplumes are now uncontested (see, e.g., ROMANOWICZ and GUNG, 2002). Whole-mantle tomography, using traditional ray theory and a large number of different ray trajectories for reflected and transmitted waves in the mantle and outer core with earthquake relocation, has increasingly yielded better images of plumes (e.g. ZHAO, 2004). MONTELLI et al. (2004, 2006) applied finite-frequency tomography, which compensates for the effects of wave diffraction, to the delays of compressional and shear waves in two frequency bands. This method takes into account the sensitivity of travel time to structure away from the ray-theoretical path, which yields better-constrained plume conduits (NOLET et al., 2007) and hence detects mantle plumes *200 to *400 km in diameter. But despite these improvements in global tomography, the lack in detailed resolution means the nature of convection in the mantle and the behaviour of mantle plumes are still uncertain. In this article my objective is to investigate in fine detail the connection between the African superplume and the upper mantle anomaly beneath East Africa by directly testing hypotheses. Previous procedures for estimating reliability and resolution in tomography models include synthetic inversions with random travel-time errors and synthetic inversions on data with travel-time residuals corresponding to a given pattern of mantle heterogeneity, the so-called checker board tests (e.g., GRAND, 1994). RITSEMA et al. (1999) have approached resolution by computing Backus Gilbert kernels for their inversions. These approaches give a good sense of the coverage of data sets in terms of raypaths or sensitivity kernels

3 Middle Mantle Seismic Structure Fig. 1 Vertical cross section to illustrate the African superplume s slow-velocity anomaly with Backus Gilbert resolution kernels for locations X, Y, and Z at 2,500, 1,500, and 700 km depth, respectively, and shells (left, after Fig. 4 in RITSEMA et al., 1999) and obliquely orientated cross sections for seismic tomography model S20RTS (right, after Fig. 1 in GURNIS et al., 2000)

4 M. B. C. Brandt Pure Appl. Geophys. but are difficult to use in directly assessing hypotheses. A further complication is that source locations are uncertain, and it is difficult to include the uncertainty in standard resolution analyses. In my investigation I test hypotheses concerning the continuity between the lower mantle African superplume and the seismically slow upper mantle beneath East Africa. Each hypothesis is directly tested by applying a constrained global tomography inversion and seeing if the misfit is significantly degraded statistically. I apply an F test to the travel-time residual s variance from numerous test models for a given data set, as well as varying a smoothing procedure to allow me to make an objective decision on the truth or falsity of the above mentioned hypotheses. I estimate the sensitivity of my method to changes in lateral size and perform an F test on the complementary data set to estimate the dependence of my method on changes in the degree of freedom. A probability plot confirms that even though the data do not follow a normal distribution, they are still valid for hypothesis testing. 2. Inversion I added 2,600 new travel-time measurements of S, SS, ScS, SKS and SKKS phases to GRAND (2002) and SIMMONS et al. (2007) data set of 41,469 phases. These data were derived from earthquakes of magnitude for the period 25 October 2007 to 19 November These earthquakes were recorded by the networks MEDNET (Istituto Nazionale di Geofisica, Italy), GEOSCOPE (Institut de Physique du Globe de Paris), AfricaArray (Pennsylvania State University, USA, The University of the Witwatersrand, South Africa and the South African Council for Geoscience), Global Telemetered Southern Hemisphere Network (USGS Albuquerque Seismological Laboratory, USA), IRIS/IDA (University of California and Scripps Institution of Oceanography, USA), and IRIS/USGS (USGS Albuquerque Seismological Laboratory, USA). The travel-time residuals of measured arrivals versus those predicted by a onedimensional starting model taken from GRAND (1994) were measured to prepare the data for the inversion. The times of the various S phases were found by computing synthetic seismograms using a WKBJ code (CHAPMAN, 1978) and aligning the peaks of the measured data and the synthetics. Earthquake locations were taken from the Harvard Centroid Moment Tensor catalogue, although the depths of the earthquakes were determined by synthetic seismogram modelling of S and ss waves. Shallow earthquakes with depths of less than 39 km were rejected because the S and ss phases became difficult to distinguish and would require more advanced analysis. Corrections for variations in crustal thickness and topography were made to the synthetic seismograms using the CRUST5.1 model (MOONEY et al., 1998). Ellipticity corrections were made for all measured times (GRAND, 1994; SIMMONS et al., 2007). Next, multiple tomographic inversions were completed with a modified simultaneous iterative reconstruction technique. The mantle was divided into blocks having uniform slowness differences, with dimensions of about km 2 laterally and with varying depth thicknesses from 75 to 150 km. The slowness difference for a particular block relative to the starting model is given by the weighted average of the slowness difference associated with each ray that passes through the block. This is only an approximate solution and is applied iteratively using the reconstruction technique to derive the final tomographic model. First, the data were inverted via 25 iterations, allowing only the upper 400 km and bottom 2,650 2,890 km of the model to vary. After the upper and very deep mantle inversion, the earthquakes were relocated in a least-squares sense using the time residuals from the heterogeneous model derived in the first step. The original data were corrected for the new source locations, and the process was repeated until the earthquake locations converged. This is a conservative procedure when estimating middle mantle heterogeneity, in that as much of the data variance as possible is explained by upper and very deep mantle variations that are thought to be larger than mid-mantle heterogeneity (GRAND, 2002). The resulting shallow three-dimensional model was then used as the starting model for an inversion, allowing the whole mantle to vary through 250 iterations. The first upper and very deep mantle inversion was smoothed with a weight of 20 for the central block in relation to the four adjacent

5 Middle Mantle Seismic Structure blocks (in the shells in two dimensions) to ensure compatibility with GRAND S (1994) previous, conservative models. The second (whole-mantle) inversion was initially also smoothed with a central weight of 20. Smoothing tests with weights of 1, 10, 20, 60 and 120 will be performed below. Note that for a high weight, less smoothing occurs. Three shells and two cross-section from the tomographic model are shown in Plate Aa e, respectively, labelled REFERENCE. These are the shallowest shell that was inverted twice (25 and 250 iterations), a middle mantle shell at 850 1,000 km depth, and the deepest shell that was also inverted twice and shows the superplume above the core mantle boundary. The mean was removed for each shell, and the shells were further smoothed (in three dimensions between shells for map production) at each point with the differences to the six adjacent blocks, and then gridded and contoured. Note that the amplitude scale varies with depth so that the velocity differences in the shallowest layers are five times larger than for the deep layers. The cross-sections that slice through the NW SE-orientated superplume along cross-cut and are marked on the maps. For example, the points labelled with x are one, possible complex link between the upper and lower anomalies interpreted graphically from cross sections and 3D animations by BEGG et al. (2009). The scale of the cross-sections is the same as those for the shells. Note the near continuity of slow velocity from the deepest mantle to the surface under East Africa. 3. Hypothesis Testing The tomographic model is derived using an iterative reconstruction technique which minimises the difference between measured and predicted traveltime residuals in a least-squares sense. Since the travel-time data are subject to random errors, and tomographic images usually need to be smoothed to enhance anomalies, a decision about the truth or falsity of any hypothesis is also subject to the quality and quantity of the data used and to the smoothing constraint used. Where the truth or falsity of a hypothesis is based on experimental evidence, statistical hypothesis testing is often performed to minimise decision errors (e.g. BAIN and ENGELHARDT, 1991; STEYN et al., 1999). Hence I construct an F test to objectively interpret the continuity of the slowvelocity anomaly from the core mantle boundary to the surface beneath eastern Africa. The statistical null hypothesis is the model where the superplume penetrates through the middle mantle (BEGG et al., 2009). This is written as H 0 (Y 0 ): s = s 0 min where Y 0 is a vector of travel-time residuals explained further below, s 2 0 is the measured-to-predicted travel-time misfits quantified by the residual s variance, and 2 s 0 min is the best-fit variance for a given data set and smoothing procedure. For hypotheses where the upper and lower mantle anomalies are separated by average mantle slowness between 670 and 1,000 km depth, I construct a test model. This is written as H m (Y m ): s 2 2 m = s m min. Y m and s 2 m are defined as before for m = 1, 2, 3,, N, where m are N different volumes of average mantle slowness situated between the anomalies that I constrain during the tomographic inversion and which I allow to vary. Both best-fit variances are defined for the same data set and smoothing procedure, where s 0 min \ s m min. I determine how valid 2 2 the derived test model is by calculating the probability of accepting false, alternative hypotheses. This is an expansion of RITSEMA et al.(1999) study. They applied Backus-Gilbert resolution kernels to determine the trade-off between resolution and stability to decide whether the middle mantle velocity structure of the superplume is resolved. To test the alternative hypotheses, I followed the same inversion procedure as described above, except that the slowness difference for each block inside an obstruction volume was constrained to be zero during the whole-mantle iterative reconstructions. I accomplished this by inverting with the perturbed ray segments that pass through these blocks set to zero. I name these regions obstruction volumes, following the suggestion of MONTELLI et al. (2004) that a thermal boundary layer divides the mantle into two convecting regions, which are linked in a complex way, unlike the simple models of either whole or layered mantle convection. The inversion result for model BLOCK-10 is shown in Plate Ba. My convention is that BLOCK-10 refers to constraining the perturbation in a volume in the 10th spherical layer

6 M. B. C. Brandt Pure Appl. Geophys. Plate A Three spherical shells from the global tomography model labelled REFERENCE (a, b and c). The shallowest and deepest shells (a and c) were inverted with 25 iterations before the whole mantle, including the shell at 850 1,000 km depth (b), was inverted with 250 iterations. The superplume is shown above the core-mantle boundary in red under and surrounding Africa (c). All shells were smoothed with a central weight of 20. An x on cross-sections 1 (d) and 1 (e) indicates a complex link between the slow-velocity anomalies. A relative scale is shown at the bottom of cross-section 2 (e) for every second layer with every fourth layer numbered: below 650 km and above 2,500 km depth the scale is the same for all the layers. Selected cross-sections from cross-cuts 1 and 2 for the various BLOCK models are included in Plates B, C and D from the top in my global tomography model to be zero. In this case, the slowness anomaly from 850 to 1,000 km depth is constrained to be zero. Mapproduction procedures cause the volume to show up as a yellow area. The corresponding cross-sections 1 and 2 are shown in Plate Bb, c. The blocks inside the obstruction volume are in black. In testing models I constrain velocity from 13 Sto28 N

7 Middle Mantle Seismic Structure Plate B Spherical shell from model BLOCK-10 at 850 1,000 km depth (a) smoothed with a central weight of 20. The volume constrained to zero during the inversions is indicated with a yellow block beneath eastern and southern Africa. The volume in (a) constrained to zero during the whole-mantle inversion is indicated in black on cross-sections 1 and 2 (b and c). A relative scale is shown at the bottom (b and c) for every second layer with every fourth layer numbered: below 650 km and above 2,500 km depth the scale is the same for all the layers and 26 to 48 E for shallow depths and from 18 S to 18 N and 16 to 42 E for deep depths. The postscript S in model names refers to deep tests between 850 and 1,600 km with different lateral extend. This area covers the African superplume below 1,300 km depth. Volume depths for the various tests are summarised in Table 1. Plate Ca f show cross-sections 1 and 2, respectively, for BLOCK models 06-07, and S. After tomographic inversions for both the null and alternative hypotheses had been completed, I defined vectors Y 0 = y 1,,y n0 and Y m = y 1,,y nm for the relevant travel-time residuals from the rays that have sampled the mth volume, where m is the corresponding BLOCK model. Since all the volumes are thin in comparison with the mantle thickness, I gave equal Test model Table 1 Volume thickness of the BLOCK models Depth (km) BLOCK BLOCK BLOCK BLOCK ,000 BLOCK ,000 BLOCK ,150 BLOCK ,300 BLOCK-12-S 1,150 1,300 BLOCK S 1,000 1,450 BLOCK S 850 1,600 BLOCK ,300 1,600 BLOCK S 1,300 1,600 The postscript S in model names refers to deep tests between 850 and 1,600 km with different lateral extent

8 M. B. C. Brandt Pure Appl. Geophys. Plate C Cross-sections 1 and 2 for models BLOCK (a and d), BLOCK (b and e) and BLOCK S (c and f) smoothed with a central weight of 20. The volume constrained to zero perturbation during the whole-mantle inversion is indicated in black. A relative scale is shown at the bottom (c and f) for every second layer with every fourth layer numbered: below 650 km and above 2,500 km depth the scale is the same for all the layers weight to each travel-time residual, even if the specific ray merely grazed the volume. For a simple singlevariable test where Y 0 and Y m are independent, have normal distributions with respective sample variances S 0 and S m, with standard deviations of the differences between measured and predicted travel-times r 0 and r m as well as degrees of freedom v 0 = n 0-1 and v m = n m - 1, the F ratio has the form (e.g. BAIN and ENGELHARDT, 1991; STEYN et al., 1999): Fðv 0 ; v m Þ S2 0 r2 m S 2 m r2 0 Evaluating F provides a test of significance between two estimates of sample variances: F * f(n 0-1, n m - 1) if H 0 (Y 0 ): s = s 0min is true. Ray paths through the mantle, excluding the volume, are the same for both respective models. Hence the number of travel-time residuals is n = n 0 = n m and thus v = v 0 = v m. If we are 95 % confident that the ratio r 0 /r m is being exceeded, then this can be written as: P S2 0 r2 m f S 2 0:95 ðv 0 ; v m Þ ¼ 0:95 m r2 0 We know that all the respective travel-time residual vectors Y 0 and Y m have variance s 2 0 less than s 2 m. Hence H 0 (Y 0 ): s 0 \ H m (Y m ): s m is always true. For this study, I perform an F test for a left-tailed, type II

9 Middle Mantle Seismic Structure error to determine the probability of accepting a false alternative hypothesis within the 5 % confidence interval around the test parameter s 2 0 /s 2 m. A large probability casts doubt on the validity of the null hypothesis (50 % means equal probability for both models), whereas a wide confidence interval around s 2 0 /s 2 m corresponds to a poor estimate (e.g. BAIN and ENGELHARDT, 1991; STEYN et al., 1999). My objective is to statistically quantify whether a connection between the lower mantle African superplume and the slow upper mantle beneath East Africa is required by the seismic data. This differs from the approach adopted by HEARN (1984) who used an F test to test the statistical significance of changing the degree of freedom by adding new parameters to his southern California crustal model. For my study, however, determining the degree of freedom is impractical. GRAND S (2002) global model currently has 51,084 travel-time measurements versus 99,146 blocks, in comparison with 2,773 blocks for the southern California crust. Smoothing increases the degree of freedom to *51,084 99,146/6 when accounting for the number of damping equations, although the central smoothing weight is also important. I consider only relevant travel-time residuals, which makes it difficult to estimate the degree of freedom for each specific hypothesis test. However, all the BLOCK models are thin in comparison with the mantle thickness and have lateral sizes that include only the slow-velocity anomaly. The number of travel-time residuals (only relevant rays) is sufficiently large in comparison with the number of blocks corrected for smoothing, p 0, for both the null hypothesis and the mantle without the respective obstruction volume, p m, so that for a thin small volume p 0 * p m. Hence F * f 0.95 (n 0 - p 0, n m - p m ) * f 0.95 (n - 1, n - 1)? f 0.95 (?,?) = 1. We can approximate the 5 % confidence interval by a simple, single-variable test. Tests for volume thickness, smoothing and lateral size are performed below with complementary hypothesis testing to estimate sensitivity to the degree of freedom. Histograms of travel-time residual vectors are shown in Fig. 2a d for REFERENCE (left) and BLOCK (right) models 06-07, , 10 and S. Volume depths for the various tests are summarised in Table 1. The corresponding shells and cross-sections are shown in Plates Ba c and Ca f. The number of residuals and various best-fit parameters are listed with the probabilities and confidence intervals. All these tests employed a central smoothing weight of 20. Note that the best-fit parameters for the REFERENCE model change slightly for each test because different rays are considered and the amount of travel-time data decreases with smaller volume size and increasing depth. BLOCK with obstruction volume in the mantle transition zone and BLOCK S with its volume in the deeper mantle have probabilities of 7.3 and 6.1 %, respectively, of accepting false, alternative hypotheses. These low probabilities with their narrow confidence levels imply that the REFER- ENCE model is valid for these depths. However, BLOCK and its thinner model at 850 1,000 km depth, BLOCK-10, have respective probabilities of 31.8 and 50.1 %. These high probabilities with their small confidence intervals cast doubt on the validity of the null hypothesis at this depth. My statistical testing indicates that a valid, alternative hypothesis, consisting of an obstruction volume of a mere 150 km thickness, may be true with the same probability as the REFERENCE model with a tenuous connection between the deep mantleand upper mantle slow velocities. My testing also confirms the validity of the slow velocities in the REFERENCE model for the deep mantle and the mantle transition zone. 4. Smoothing and Lateral Size My hypothesis tests are based on travel-time data which are subject to random errors. Sources of error include origin time, location and phase pick. In addition, any global tomographic inversion problem is always underdetermined because of the limited geographical distribution of suitable earthquake sources along, e.g., plate boundaries and due to uneven distribution of seismometers, especially the small numbers in the oceans. I apply smoothing with every iterative reconstruction decreasing the degree of freedom. Smoothing, however, could suppress small anomalies and may destroy the fine detail in a large anomaly hence smoothing is important for my

10 M. B. C. Brandt Pure Appl. Geophys. Fig. 2 a Histogram of travel-time residuals for model REFERENCE (left, labelled 0 for vector Y 0 ) and BLOCK (right) smoothed with a central weight of 20. Residuals are grouped into bins of 1 ms. The number of residuals (N) with best-fit parameters maximum (max), the mean, mean of the absolute values ( mean ), standard deviation (std), variance (var) and minimum (min) are listed on the inside of the histogram and the probability and confidence interval at the bottom. For graphical presentations of BLOCK see Plate Ca, d. b Histogram of travel-time residuals for model REFERENCE (left, labelled 0 for vector Y 0 ) and BLOCK (right) smoothed with a central weight of 20. Residuals are grouped into bins of 1 ms. The number of residuals (N) with best-fit parameters maximum (max), mean, mean of the absolute values ( mean ), standard deviation (std), variance (var) and minimum (min) are listed on the inside of the histogram and the probability and confidence interval at the bottom. For graphical presentations of BLOCK see Plate Cb, e. c Histogram of traveltime residuals for model REFERENCE (left, labelled 0 for vector Y 0 ) and BLOCK-10 (right) smoothed with a central weight of 20. Residuals are grouped into bins of 1 ms. The number of residuals (N) with best-fit parameters maximum (max), mean, mean of the absolute values ( mean ), standard deviation (std), variance (var) and minimum (min) are listed on the inside of the histogram and the probability and confidence interval at the bottom. For graphical presentations of BLOCK-10 see Plate Ba c. d Histogram of travel-time residuals for model REFERENCE (left, labelled 0 for vector Y 0 ) and BLOCK S (right) smoothed with a central weight of 20. Residuals are grouped into bins of 1 ms. The number of residuals (N) with best-fit parameters maximum (max), mean, mean of the absolute values ( mean ), standard deviation (std), variance (var) and minimum (min) are listed on the inside of the histogram and the probability and confidence interval at the bottom. For graphical presentations of BLOCK S see Plate Cc f

11 Middle Mantle Seismic Structure Fig. 3 a Histogram of travel-time residuals for model REFERENCE (left, labelled 0 for vector Y 0 ) and BLOCK (right) smoothed with a central weight of 1. Residuals are grouped into bins of 1 ms. The number of residuals (N) with best-fit parameters maximum (max), mean, mean of the absolute values ( mean ), standard deviation (std), variance (var) and minimum (min) are listed on the inside of the histogram and the probability and confidence interval at the bottom. For a graphical presentation of BLOCK see Plate Da. b Histogram of travel-time residuals for model REFERENCE (left, labelled 0 for vector Y 0 ) and BLOCK (right) smoothed with a central weight of 120. Residuals are grouped into bins of 1 ms. The number of residuals (N) with best-fit parameters maximum (max), mean, mean of the absolute values ( mean ), standard deviation (std), variance (var) and minimum (min) are listed on the inside of the histogram and the probability and confidence interval at the bottom. For a graphical presentation of BLOCK see Plate Db study since alternative hypothesis BLOCK-10 is very thin. A decision to accept or reject a hypothesis from an F test is based on the test parameter s 0 2 /s m 2. In turn, the residual data variance depends on the amount of smoothing. By repeating the whole-mantle inversions for both REFERENCE and BLOCK models with central smoothing weights of 1, 10, 20, 60 and 120, I can estimate the effect of smoothing. Figure 3a, b are example histograms of travel-time residual vectors for models REFERENCE and BLOCK smoothed with central weights of 1 and 120, respectively. Best-fit parameters and the probability and confidence interval have the same meaning as before. Cross-sections 1 for both respective models are included in Plate Da b. Note how rough the image of cross-section 1 in Plate Db appears in comparison with that in Plate Da, which was smoothed with a central weight of 1. The results of the smoothing are summarised in Fig. 4a, b for all the models with their depths listed in Table 1. Variances for the respective REFERENCE models (stars), BLOCK models (crosses) and probability at 5 % significance (triangles) are presented as a function of the central smoothing weight. A trend observed for Plate D Cross-section 1 for model BLOCK smoothed with a central weight of 1 (a) and a weight of 120 (b). The volume constrained to zero perturbation during the whole-mantle inversion is indicated in black. A relative scale is shown at the bottom (b) for every second layer with every fourth layer numbered: below 650 km and above 2,500 km depth the scale is the same for all the layers

12 M. B. C. Brandt Pure Appl. Geophys. Fig. 4 a Variances for the respective REFERENCE models (stars) and BLOCK models (crosses) and probability at 5 % significance (triangles) asa function of the central smoothing weight. BLOCK models shown are: 08 (top left), (top middle), (top right), 10 (bottom left), (bottom middle), and (bottom right). b Variances for the respective REFERENCE models (stars) and BLOCK models (crosses) and probability at 5 % significance (triangles) as a function of the central smoothing weight. BLOCK models shown are: 12-S (top left), S (top middle), S (top right), (bottom left), and S (bottom right). The variances and probabilities for model BLOCK are plotted on top of those for model BLOCK S with a dash-dot line every REFERENCE and BLOCK model is that variance decreases with less smoothing. Variances are consistently lower for REFERENCE models than for their corresponding BLOCK models. Model BLOCK at km depth has medium probability (20 24 %), and corresponding thin BLOCK-08 s probabilities vary between 36.0 and 44.2 %. All probabilities for thick model at 400 1,000 km depth are very low (\5 %). BLOCK-10 actually has a slightly higher probability ([50 %) than the null hypothesis for smoothing weights of 1, 10 and 20; for smoothing weights of 60 and 120 the probability remains above 45.1 %. Thicker models and have low to medium probabilities. The probability for mantle transition zone model BLOCK is much lower than that for shallow model All the other deep models have lower probabilities and only 12-S goes above 20 %. Consistent probabilities for all the weights led me to conclude that smoothing does not adversely affect my hypothesis testing and also demonstrates the advantage of statistical testing to a graphical interpretation of smoothed, tomographic images. Another important issue is the effect of lateral size on the hypothesis testing. Specifically, we need to know how sensitive the outcome is to a volume that extends beyond the slow-velocity anomaly. BLOCK has the same lateral size as the shallower models but, due to the superplume s tilt towards the south west with depth, the volume extends to outside the plume. The corresponding best-fit parameters for REFERENCE and BLOCK models S and in Figs. 2d and 3a, b have different values yet have similar, low probabilities. The variances and probabilities for BLOCK are plotted on top of the results for S with a dash dot line in Fig. 4b. The low percentage probabilities indicate that reasonable changes in lateral size do not cause significant changes to the statistical probability. This was also confirmed with extended volumes for the other BLOCK models not shown here. Another clear trend is the probability decrease with volume thickness for a set of models from thin (BLOCK-08, -10, and -12-S) to thick (BLOCK , , and S) volumes. This raises the question: Are my results merely an artefact of changing the degree of freedom? I therefore performed F tests for a two-tailed, type I error to determine the probability that the variances of the complementary rays that did not sample the volume are the same for the null (REF- ERENCE) and alternative hypotheses (BLOCK models) within the 5 % confidence interval. A 100 %

13 Middle Mantle Seismic Structure probability means that the complementary variances are identical, whereas a low value implies that the Earth model surrounding the rays that have sampled the volume differs significantly from the inverted model. Graphs corresponding to Fig. 4a, b are shown in Fig. 5a, b in which each test consists of *48,000 travel-time residuals and *99,146 minus 140 to 720 blocks. Complementary variances for the respective REFERENCE models (stars) and BLOCK models (crosses), and the complementary probability at 5 % significance (triangles) are presented as a function of the central smoothing weight. The complementary variances are so similar that they plot on top of one another in all the graphs. The complementary probability decreases with smoothing weight and volume thickness for all three sets of tests. For example, the complementary rays for BLOCK-10 have the highest probability of 96.5 % for a smoothing weight of 1, and those for BLOCK have the lowest probability of 53.0 % for a weight of 60. Models and S, which have different lateral sizes, have complementary variances and probabilities similar to those in Fig. 4b. Given the insignificant size of the obstruction volume with its surrounding, sampled mantle in comparison with the whole Earth model, I conclude that all the thick volumes cause the tomographic inversion to recover a complementary model, which differs significantly from the inverted model. However, thin volume BLOCK-10 with high complementary probability is not affected by the change in the degree of freedom and hence represents the real Earth. An F test assumes samples of data vectors from a normal distribution (e.g. BAIN and ENGELHARDT, 1991; STEYN et al., 1999), but this is not the case here. Figure 6 shows the probability plot of the travel-time residuals of BLOCK-10 to graphically assess whether the data come from a normal distribution. The smoothing weights of 1 to 120 are plotted on top of one another (dots) in comparison with the first and third quartiles of their normal distributions (dash dot lines). The distribution of travel-time residuals deviates for BLOCK-10 (and all the models not shown here) from the normal distribution at high probability in that more travel-time residuals are near the mean, and at low probability in that there are fewer traveltime residuals from outliers. Less smoothing causes the slope of the normal distribution lines to increase and thus the higher the smoothing weight, the closer the data resemble a normal distribution. If we assume a normal error distribution for the raw tomography travel-time residuals, then smoothing not only Fig. 5 a Complementary variances for the respective REFERENCE models (stars) and BLOCK models (crosses) and complementary probability at 95 % significance (triangles) as a function of the central smoothing weight. BLOCK models shown are: 08 (top left), (top middle), (top right), 10 (bottom left), (bottom middle), and (bottom right). b Complementary variances for the respective REFERENCE models (stars) and BLOCK models (crosses) and complementary probability at 5 % significance (triangles) asa function of the central smoothing weight. BLOCK models shown are: 12-S (top left), S (top middle), S (top right), (bottom left), and S (bottom right). The complementary variances and probabilities for model BLOCK are plotted on top of those for model BLOCK S with a dash dot line

14 M. B. C. Brandt Pure Appl. Geophys. Fig. 6 Probability plot of the travel-time residuals of hypothesis BLOCK- 10 for central smoothing weights of 1, 10, 20, 60 and 120 plotted on top of one another (dots) in comparison with a normal distribution probability plot (dash dot line). The probability plot slopes become progressively steeper, more closely resembling a normal distribution, with increasing central smoothing weight removes outliers, but also filters out increasingly more well-behaved data with lower weights. The distributions are similar, smooth and nearly symmetrical around the mean between the variations of maximum and minimum. Since variance is sensitive to outliers (smoothed out), and since the means of the absolute values and the standard deviation are less for the null hypothesis in every test (e.g., Figs. 2a d, 3a, b), I believe that the F test is an appropriate technique for my study. 5. Discussion Fig. 7 a Histogram of travel-time residuals for complete (through and complementary) model REFERENCE (left, labelled 0 for vector Y 0 ) and complete (through and complementary) BLOCK-10 (right) smoothed with a central weight of 20. Residuals are grouped into bins of 1 ms. A two second time difference is subtracted from the residuals of the rays that pass through the obstruction volume (right) which represents a relative faster velocity for the volume (obstruction). The number of residuals (N) with best-fit parameters maximum (max), mean, mean of the absolute values ( mean ), standard deviation (std), variance (var) and minimum (min) are listed on the inside of the histogram and the probability and confidence interval at the bottom. b Variances for the complete (through and complementary) REFERENCE model (stars) and complete (through and complementary) BLOCK-10 model (crosses) and complete probability at 5 % significance (triangles) for a fixed central smoothing weight of 20 as a function of the time difference (s). A time difference is subtracted or added from the residuals of the rays that pass through the obstruction volume. A negative time difference represents a relative faster velocity for the volume (obstruction) whereas a positive difference represents a slower velocity (connection) As an alternative hypothesis to the African superplume extending from the core mantle boundary through the mantle transition zone into the slow-velocity anomaly in the upper mantle, I accepted a model with a thin, small obstruction volume at 850 1,000 km depth with equal probability to the inverted tomographic model. All other tests in Fig. 4a, b had lower probabilities. To definitively answer the question of whether or not the slow velocities in the shallow mantle are connected to the deeper superplume, I test another, alternative hypothesis where a connection is forced at 850 1,000 km depth. I followed the same hypothesistesting procedure as described above, except that I considered all the travel-time residuals (rays that passed through the volume and complementary rays) and subtracted a time difference of 2 s from the residuals of

15 Middle Mantle Seismic Structure the rays that pass through the volume. Note that a negative time difference represents a relative faster velocity for the volume (obstruction), whereas a positive difference represents a slower velocity (connection). The histograms of travel-time residual vectors are shown in Fig. 7a for the complete REFERENCE (left) and complete, 2 s subtracted, BLOCK-10 (right) model. Variances for the complete REFERENCE model (stars), complete, added or subtracted, BLOCK-10 models (crosses) and probability at 5 % significance (triangles) are presented in Fig. 7b. The central smoothing weight is fixed to 20 and only the time difference varies. The variance is at a minimum and the probability has a maximum of 41.2 % for a time difference of -2 s. The minimum variance is significantly lower and maximum probability much higher than for a connection with time differences of more than 0 s. Hence, an obstruction between the shallow mantle slow velocities and the deeper superplume is more likely than a connection. My result agrees with that of RITSEMA et al. (1999), namely that the superplume could be weak in the middle mantle, but differs in that I find a very thin weak zone rather than a weakening between 670 and 1,000 km depth. I conclude that the African superplume rises to at least 1,150 km depth (more likely to 1,000 km). A mantle transition zone beneath the East African Rift with an unusual thickness would indicate a thermal anomaly within the deep upper mantle (e.g., BINA and HELFFRICH, 1994). Upper mantle seismic velocity variations beneath northern Tanzania have measured a wide depression of the 410 km discontinuity but a flat 660 km discontinuity and an average zone thickness of 235 km consistent with the slow velocities in the shallow mantle (RITSEMA et al., 1998b; NYBLADE et al., 2000; VENKATARAMAN et al., 2004). The thickness close to the global average of 242 km (e.g., LAWRENCE and SHEARER, 2006) indicates a mantle transition zone near average global temperature and chemical composition (e.g., BINA and HELFFRICH, 1994). To definitively answer the question whether or not the transition zone acts as an obstruction between the African superplume and the shallow mantle slow velocities I completed hypothesis test BLOCK with depth at km (Table 1; Fig. 2a). The very low probability of 7.3 % for an alternative model with an obstruction let me to conclude that the shallow slow-velocity anomaly continues from the surface to below the mantle transition zone as proposed by RITSEMA et al. (1998a, b) and NYBLADE et al. (2000). On the other hand it also implies that the transition zone would not act as an obstruction to a possibly rising African superplume. My results are in accord with the global catalogue of different mantle plume varieties by MONTELLI et al. (2004). They identified areas where deep mantle plumes occur below hotspots, other areas where plumes only reach the mid-mantle, and yet other areas where plumes are confined to the upper mantle. The African superplume is similar to the first case in that it originates at the core mantle boundary and is capped by the Afar hotspot in eastern Africa. It is different in that the data does not require slow velocities in the middle mantle to connect the two regimes. Alternatively, the superplume could consist of two separate lower and upper mantle plumes, with the upper plume originating below the 670 km discontinuity. This is similar to another variety of plume also capped by hotspots which has its base near the mantle transition zone. However, the obstruction volume s thickness of only 150 km and the dynamic, high topography of the African superswell (LITHGOW-BERTELLONI and SILVER, 1998; FORTE et al., 2010) argue against a complete separation into two convecting regions. The seismic velocities inside the superplume are slower than normal, indicating that the structure may be hotter than the surrounding mantle and/or may include chemical changes (e.g., SIMMONS et al., 2007). Detailed waveform analyses have revealed that the plume possesses a ridge-like morphology and abrupt wave speed reductions near its boundaries. Slow velocities may indicate high temperatures, but the morphology and abrupt velocity jumps associated with the structure cannot be easily attributed to temperature variations alone, implying potential chemical changes. This hypothesized chemical component means that at least part of the superplume is denser than the surrounding mantle, which slows its rise upward (e.g., NI et al., 2002, 2005; NI and HELMBERGER, 2003). The thermally induced density perturbations are greater in magnitude then the chemically induced, implying overall positive

16 M. B. C. Brandt Pure Appl. Geophys. buoyancy throughout the superplume, but may be deforming under the influence of its intrinsic negative chemical buoyancy (SIMMONS et al., 2007). Hence, the obstruction volume at 850 1,000 km depth may be the upper limit to which the superplume can rise in the mantle. In that case, the slow velocities underlying the East African Rift would be unconnected to the deeper superplume. 6. Conclusion I developed procedures for statistical hypothesis testing to investigate whether the travel-time data require that the tilted, slow-velocity anomaly in the deep mantle under southern Africa extends into the slow-velocity anomaly in the upper mantle under eastern Africa. Testing found a thin zone where the S-velocity may be anomalously reduced above the African superplume and below the mantle transition zone. I determined that the upper mantle slowvelocity anomaly continues from the surface to below the mantle transition zone. Acknowledgments I wish to thank Prof. Grand of the University of Texas at Austin, USA. During my visits to Texas he made his tomography data set available for my research and suggested this project to me. Prof. Grand also kindly helped me to modify his inversion code to prepare the BLOCK models for my hypothesis testing. Nathan Simmons set up for my use his MatTimes 1 code to calculate predicted travel times with a one-dimensional velocity model and to measure the observed phase arrivals. I thank the University of the Witwatersrand, South Africa, for providing administrative support and the Council for Geoscience, South Africa, for granting me study leave to spend time at the University of Texas at Austin. Prof. Ray Durrheim critically checked the grammar and scientific writing of the manuscript. Two anonymous reviewers 1 MatTimes: A MATLAB-based seismic travel-time calculation and visualisation toolbox. The Department of Geosciences at Texas Tech University. and the editor suggested thoughtful improvements to the original manuscript. REFERENCES BAIN, L. J. and M. ENGELHARDT, 1992, Introduction to Probability and Mathematical Statistics, 2nd ed. The Duxbury Advanced Series in Statistics and Decision Theory, PWS-Kent Publishing Co, Boston, USA, 644 pp. BEGG, G. C., W. L. GRIFFIN, L. M. NATAPOV, S. Y. O REILLY, S. P. GRAND, C.J.O NEILL, J.M.A.HRONSKY, Y.POUDJOM DJOMANI, C. J. SWAIN, T. DEEN and P. BOWDEN, 2009, The lithospheric architecture of Africa: Seismic tomography, mantle petrology, and tectonic evolution, Geosphere, 5, BINA, C. R. and G. HELFFRICH, 1994, Phase transition Clapeyron slopes and transition zone seismic discontinuity tomography, Journal of Geophysical Research, 99, 15,853 15,860. CHAPMAN, C. H., 1978, A new method for computing synthetic seismograms, Geophysical Journal of the Royal Astronomical Society, 5, 4, FORTE, A. M., S. QUÉRÉ,R.MOUCHA,N.A.SIMMONS,S.P.GRAND,J. X. MITROVICA and D. B. ROWLEY, 2010, Joint seismic-geodynamic-mineral physical modeling of African geodynamics: A reconciliation of deep-mantle convection with surface geophysical constraints, Earth and Planetary Science Letters, 295, , doi: /j.epsl GRAND, S. P., 1994, Mantle shear structure beneath the Americas and surrounding oceans, Journal of Geophysical Research, 99, B6, 11,591 11,621. GRAND, S. P., 2002, Mantle shear-wave tomography and the fate of subducted plates, Philosophical Transactions of the Royal Society of London, 360, GU, Y. J., A. M. DZIEWONSKI, W.SU and G. EKSTROM, 2001, Models of the mantle shear velocity and discontinuities in the pattern of lateral heterogeneity, Journal of Geophysical Research, 106, 11,169 11,199. GURNIS, M., J. X. MITROVICA, J. RITSEMA and H. VAN HEIJST, 2000, Constraining mantle density structure using geological evidence of surface uplift rate: The case of the African Superplume, Geochemistry Geophysics Geosystems, 1, 1020, doi: / 1999GC HEARN, T. M., 1984, Pn travel times in southern California, Journal of Geophysical Research, 89, HELMBERGER, D., S. NI, L. WEN and J. RITSEMA, 2000, Seismic evidence for ultra-low velocity zones beneath Africa and eastern Atlantic, Journal of Geophysical Research, 105, 23,865 23,878. KING, S. D. and J. RITSEMA, 2000, African hot spot volcanism: Scale-scale convection in the upper mantle beneath cratons, Science, 290, LAWRENCE, J. F. and P. M. SHEARER, 2006, A global study of transition zone thickness using receiver functions, Journal of Geophysical Research, 111, doi: /2005jb LITHGOW-BERTELLONI, C. and P. G. SILVER, 1998, Dynamic topography, plate driving forces and the African superswell, Nature, 395, MASTERS, T. G., G. LASKE, H. BOLTON and A. DZIEWONSKI, 2000, The relative behaviour of shear velocity, bulk sound speed and compressional velocity in the mantle: Implications for chemical thermal structure, in Earth s deep interior. Mineral physics and